blob: ebdbbe71ecc4439602cdf763a24006f44b1139a2 (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
|
\documentclass[fleqn]{article}
\usepackage[left=1in, right=1in, top=1in, bottom=1in]{geometry}
\usepackage{mathexam}
\usepackage{amsmath}
\ExamClass{Sample Class}
\ExamName{Sample Exam}
\ExamHead{\today}
\let\ds\displaystyle
\begin{document}
\ExamInstrBox{
Please show \textbf{all} your work! Answers without supporting work will not be given credit. Write answers in spaces provided. You have 1 hour and 50 minutes to complete this exam.}
\ExamNameLine
\begin{enumerate}
\item Calculate the following limits. If a limit is $\infty$ or $-\infty$,
please say so. Make sure you show all your work and justify all your
answers.
\begin{enumerate}
\item $\ds{\lim_{x\rightarrow3}\frac{\sqrt{x+1} - 2}{x-3}}$\answer
\item $\ds{\lim_{x\rightarrow0}\frac{\sin(4x)}{8x}}$\answer
\end{enumerate}
\item Use the $\varepsilon$-$\delta$ definition of limit to prove that
\[\lim_{x\rightarrow 2} x^2 - 3x + 2 = 0\]\noanswer[2.5in]
\newpage
\item If $h(x) = \sqrt{x^2 + 2} - 1$, find a \textbf{non-trivial} decomposition of $h$ into $f$ and $g$ such that $h = f\circ g$.
\answer*{$f(x)=$}\addanswer*{$g(x)=$}
\item Find the first two derivatives of the function $f(x) = x^2\cos(x)$. Simplify
your answers as much as possible. Show all your work.
\answer*{$f'(x)=$}\answer*{$f''(x)=$}
\newpage
\item Find the derivative of the function $\ds{f(x) = \int_{x^2}^2
\frac{\cos(t)}{t} \,dt}$.\answer[1in plus 1fill]
\item Set up, but do not evaluate, the integral for the volume of the solid obtained by rotating the area between the curves $y = x$ and $y = \sqrt{x}$ about the $x$-axis.\noanswer
\end{enumerate}
\end{document}
|
